1. Field of the Invention
The present invention relates to an integrated circuit using logarithmic amplifiers, which may be used in a color sensor.
2. Description of the Related Art
A typical conventional circuit using logarithmic amplifiers will be described with reference to FIG. 1.
In FIG. 1, the output of a logarithmic amplifier LOG1 is connected through a resistor R.sub.1 to the inverting input terminal of an operational amplifier AMP1. The output of another logarithmic amplifier LOG2 is connected through a resistor R.sub.3 to the noninverting input terminal of operational amplifier AMP1. Output e.sub.1 of amplifier LOG1 is fed back to the inverting input terminal of the amplifier LOG1, via a diode D.sub.1. Similarly, output e.sub.2 of amplifier LOG2 is fed back to the inverting input terminal of amplifier LOG2 via a diode D.sub.2.
In this conventional circuit, output e.sub.1 of amplifier LOG1 is expressed as: EQU e.sub.1 =V.sub.T ln (I.sub.f1 /I.sub.s1) (1)
and output e.sub.2 of amplifier LOG2 likewise is expressed as: EQU e.sub.2 =V.sub.T ln (I.sub.f2 /I.sub.s2) (2)
where I.sub.f1 and I.sub.f2 designate the current flowing through the feedback circuits, via diodes D.sub.1 and D.sub.2, of amplifiers LOG1 and LOG2, respectively. I.sub.s1 and I.sub.s2 designate the reverse saturation current of diodes D.sub.1 and D.sub.2, respectively. V.sub.T =KT/q, where "q" represents a quantity of charge as given by 1.6.times.10.sup.-19 (C), K the Boltzmann constant as given by 1.38.times.10.sup.-23 (J/K), and T an absolute temperature.
Output e.sub.0 of operational amplifier AMP1 is expressed as: ##EQU1## If R.sub.1 =R.sub.3 and R.sub.2 =R.sub.4, and no matching error exists with respect to resistors R.sub.1 and R.sub.2, output e.sub.0 becomes: ##EQU2## Substituting equations (1) and (2) for equation (4), e.sub.0 can be written as: ##EQU3##
Equation (5) is obtained on the assumption that R.sub.1 =R.sub.3 and R.sub.2 =R.sub.4, and no matching errors exist with respect to resistors R.sub.1 and R.sub.2. The matching error, however, exists in a semiconductor integrated circuit and causes a gain error. If the matching error is considered so that the resistance of each resistor is defined as:
R.sub.1 =R.sub.1 +.DELTA.R.sub.1 PA1 R.sub.2 =R.sub.2 +.DELTA.R.sub.2 PA1 R.sub.3 =R.sub.1 +.DELTA.R.sub.3 PA1 R.sub.4 =R.sub.2 +.DELTA.R.sub.4
then equation (3) becomes equation (6)' shown in Table 1. For obtaining the error component contained in the output voltage, equation (6)' is modified as equation (6)" shown in Table 1. Substituting equations (1) and (2) for equation (6)", we have equation (6) as shown in Table 1, where A and B are defined as: ##EQU4##
TABLE 1 __________________________________________________________________________ equation (6)' equation (6)" ##STR1## ##STR2## equation (6) ##STR3## ##STR4## ##STR5## __________________________________________________________________________
In equation (6), the term A represents the error component of output signal e.sub.0, resulting from the matching error with respect to resistors R.sub.1 and R.sub.2 and the term B with respect to resistors R.sub.1, R.sub.2, R.sub.3 and R.sub.4.
For example, if we assume that the matching error is 3% at a maximum, so that when R.sub.1 =R.sub.2 =1 kilo-ohm, .DELTA.R.sub.1 =0 ohm, .DELTA.R.sub.2 =30 ohms, .DELTA.R.sub.3 =30 ohms, and .DELTA.R.sub.4 =-30 ohms, then the terms A and B in equation (6) become: A=1.03 and B=-0.04635.
Furthermore, if we assume that I.sub.f1 =10 uA, I.sub.f2 =20 uA, I.sub.s1 =I.sub.s2 =3.5.times.10.sup.-16 A, and V.sub.T =0.0257 V, then, the term B.multidot.V.sub.T ln (I.sub.f2 /I.sub.s2) in equation (6) becomes EQU .vertline.B.multidot.V.sub.T ln (I.sub.f2 /I.sub.s2).vertline.=0.0295 V
On the other hand, if we assume that no matching error exists, then equation (3) gives voltage e.sub.0 as: EQU e.sub.0 =0.0178 V (3)'
That is, the error component is larger than the output voltage obtained from equation (3) where no matching error with respect to resistors was assumed to exist. This indicates that the circuit in FIG. 1 will produce and output signal containing a large error resulting from the matching error with respect to the resistors, inherent in the semiconductor integrated circuit.
FIG. 2 shows an application of the conventional circuit shown in FIG. 1 to an amplifier circuit for a color sensor. In this circuit, a photo diode R-PD is connected between the inverting and noninverting input terminals of a logarithimic amplifier LOG/R. Another photo diode G-PD is connected between the inverting and noninverting input terminals of another logarithmic amplifier LOG/G. The front face of photo diodes R-PD and G-PD are covered with red (R) and green (G) color filters, respectively. Light is transmitted through these color filters before being transformed into photo currents I.sub.shR and I.sub.shG.
In FIG. 2, photo currents I.sub.shR and I.sub.shG are fed back, via diodes D.sub.R and D.sub.G, respectively, into logarithmically compressed voltages. The output terminals of logarithmic amplifiers LOG/G and LOG/R are coupled with the noninverting input terminal and the inverting input terminal, respectively, of an operational amplifier AMP3. The output voltage containing the photo current ratio of (I.sub.shG /I.sub.shR) as a color difference signal appears at output e.sub.0 of amplifier AMP3. Output e.sub.0 includes the error component as shown in equation (6) of Table 1. However, the ratio (I.sub.shG /I.sub.shR) in the color sensor varies very minutely. Furthermore, the second term of equation (6) varies with the voltage at the noninverting input terminal of amplifier AMP3. Therefore, the second term in equation (6) cannot be treated as a mere offset. This causes a large error in the final output voltage.